Resolved simulations of submarine avalanches with a simple soft-sphere / immersed boundary method

Physical mechanisms at the origin of the transport of solid particles in a fluid are still a matter of debate in the physics community. Yet, it is well known that these processes play a fundamental role in many natural configurations, such submarines landslides and avalanches, which may have a significant environmental and economic impact. The goal here is to reproduce the local dynamics of such systems from the grain scale to that of thousands of grains approximately. To this end a simple soft-sphere collision / immersed-boundary method has been developed in order to accurately reproduce the dynamics of a dense granular media collapsing in a viscous fluid. The fluid solver is a finite-volume method solving the three-dimensional, time-dependent Navier-Stokes equations for a incompressible flow on a staggered. Here we use a simple immersed-boundary method consisting of a direct forcing without using any Lagrangian marking of the boundary, the immersed boundary being defined by the variation of a solid volume fraction from zero to one. The granular media is modeled with a discrete element method (DEM) based on a multi-contact soft-sphere approach. In this method, an overlap is allowed between spheres which mimics the elasto-plastic deformation of real grain, and is used to calculate the contact forces based on a linear spring model and a Coulomb criterion. Binary wall-particle collisions in a fluid are simulated for a wide range of Stokes number ranging from 10-¹ to 10⁴. It is shown that good agreement is observed with available experimental results for the whole range of investigated parameters, provided that a local lubrication model is used when the distance of the gap between the particles is below a fraction of the particle radius. A new model predicting the coefficient of restitution as a function of the Stokes number and the relative surface roughness of the particles is proposed. This model, which makes use of no adjustable constant, is shown to be in good agreement with available experimental data. Finally, simulations of dense granular flows in a viscous fluid are performed. The present results are encouraging and open the way for a parametric study in the parameter space initial aspect ratio - initial packing

Fast calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion

This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of Wu and Zhang (2006), especially on the moment generating function, and second the approximation of density distributions based on Edgeworth or Gram-Charlier expansions. By exploring the analytical tractability of moments up to fourth order, we are able to perform an adjustment of the reference Bachelier model with normal volatilities for skewness and kurtosis, and as a by-product to derive a smile formula relating the volatility to the moneyness with interpretable parameters. As a main conclusion, our numerical results show a 98% reduction in computational time for the DD-SV-LMM calibration process compared to the classical numerical integration method developed by Heston (1993)

Simulation of an avalanche in a fluid with a soft-sphere / immersed boundary method including a lubrication force.

The present work aims at reproducing the local dynamics of a dense granular media evolving in a viscous fluid from the grain scale to that of thousands of grains, encountered in environmental multiphase flows. To this end a soft-sphere collision / immersed-boundary method is developed. The methods are validated alone through various standard configurations including static and dynamical situations. Then, simulations of binary wall-particle collisions in a fluid are performed for a wide range of Stokes number ranging in [10-1, 104]. Good agreement with available experimental data is found provided that a local lubrication model is used. Finally, three-dimensional simulations of gravity/shear-driven dense granular flows in a viscous fluid are presented. The results open the way for a parametric study in the parameter space initial aspect ratio - initial packing

Modelling the normal bouncing dynamics of spheres in a viscous fluid

Bouncing motions of spheres in a viscous fluid are numerically investigated by an immersed boundary method to resolve the fluid flow around solids which is combined to a discrete element method for the particles motion and contact resolution. Two well-known configurations of bouncing are considered: the normal bouncing of a sphere on a wall in a viscous fluid and a normal particle-particle bouncing in a fluid. Previous experiments have shown the effective restitution coefficient to be a function of a single parameter, namely the Stokes number which compares the inertia of the solid particle with the fluid viscous dissipation. The present simulations show a good agreement with experimental observations for the whole range of investigated parameters. However, a new definition of the coefficient of restitution presented here shows a dependence on the Stokes number as in previous works but, in addition, on the fluid to particle density ratio. It allows to identify the viscous, inertial and dry regimes as found in experiments of immersed granular avalanches of Courrech du Pont et al. Phys. Rev. Lett. 90, 044301 (2003), e.g. in a multi-particle configuration

Inverse reinforcement learning to control a robotic arm using a Brain-Computer Interface

The goal of this project is to use inverse reinforce- ment learning to better control a JACO robotic arm developed by Kinova in a Brain-Computer Interface (BCI). A self-paced BCI such as a motor imagery based-BCI allows the subject to give orders at any time to freely control a device. But using this paradigm, even after a long training, the accuracy of the classifier used to recognize the order is not 100%. While a lot of studies try to improve the accuracy using a preprocessing stage that improves the feature extraction, we work on a post- processing solution. The classifier used to recognize the mental commands will provide as outputs a value for each command such as the posterior probability. But the executed action will not only depend on this information. A decision process will also take into account the position of the robotic arm and previous trajectories. More precisely, the decision process will be obtained applying an inverse reinforcement learning (IRL) on a subset of trajectories specified by an expert. At the end of the workshop, the convergence of the inverse reinforcement algorithm has not been achieved. Nevertheless, we developed a whole processing chain based on OpenViBE for controlling 2D- movements and we present how to deal with this high dimensional time series problem with a lot of noise which is unusual for the IRL community

Modelling the dynamics of a sphere approaching and bouncing on a wall in a viscous fluid

The canonical configuration of a solid particle bouncing on a wall in a viscous fluid is considered here, focusing on rough particles as encountered in most of the laboratory experiments or applications. In that case, the particle deformation is not expected to be significant prior to solid contact. An immersed boundary method (IBM) allowing the fluid flow around the solid particle to be numerically described is combined with a discrete element method (DEM) in order to numerically investigate the dynamics of the system. Particular attention is paid to modelling the lubrication force added in the discrete element method, which is not captured by the fluid solver at very small scale. Specifically, the proposed numerical model accounts for the surface roughness of real particles through an effective roughness length in the contact model, and considers that the time scale of the contact is small compared to that of the fluid. The present coupled method is shown to quantitatively reproduce available experimental data and in particular is in very good agreement with recent measurement of the dynamics of a particle approaching very close to a wall in the viscous regime St <O(10), where St is the Stokes number which represents the balance between particle inertia and viscous dissipation. Finally, based on the reliability of the numerical results, two predictive models are proposed, namely for the dynamics of the particle close to the wall and the effective coefficient of restitution. Both models use the effective roughness height and assume the particle remains rigid prior to solid contact. They are shown to be pertinent to describe experimental and numerical data for the whole range of investigated parameters

Couplage IBM/DEM pour la modélisation des milieux granulaires dans un fluide

La physique des milieux granulaires denses immergés est à l'heure actuelle un domaine privilégié de la mécanique des fluides en raison des enjeux environnementaux et industriels importants associés. La dynamique d'un système dense d'objets solides en mouvement dans un fluide est particulièrement complexe car elle résulte d'interactions particule-fluide et particule-particule à petite échelle (fraction de la taille des particules), donnant lieu à des phénomènes de plus grande échelle (allant jusqu'au système complet). L'objectif ici est d'améliorer la compréhension de ces milieux via une modélisation à petite échelle, allant d'un grain à quelques milliers de grains, via le développement d'une méthode aux éléments discrets (DEM) couplée à une méthode de type frontières immergées (IBM), la première reproduisant les interactions solide-solide, la seconde les interactions solide-fluide. L'étude du rebond d'une particule sur une paroi montre que l'ajout d'une force de lubrification au voisinage du contact est nécessaire pour reproduire les cas réels. L'outil numérique ainsi validé est utilisé pour simuler un écoulement granulaire sur plan incliné dans un fluide

Fast imbalanced binary classification: a moment-based approach

In this paper, we consider the problem of imbalanced binary classification in which the number of negative examples is much larger than the number of positive examples. The two mainstream methods to deal with such problems are to assign different weights to negative and positive points or to subsample points from the negative class. In this paper, we propose a different approach: we represent the negative class by the two first moments of its probability distribution (the mean and the covariance), while still modeling the positive class by individual examples. Therefore, our formulation does not depend on the number of negative examples, making it suitable to highly imbalanced problems and scalable to large datasets. We demonstrate empirically, on a protein classification task and a text classification task, that our approach achieves similar statistical performance than the two mainstream approaches to imbalanced classification problems, while being more computationally efficient